Constraints from flavour changing neutral currents are discussed in the context of predictive Grand Unified Supersymmetric Theories. Uncertainties in the estimation of their amplitudes are minimized by using a successful mass matrix ansatz which predicts the arbitrary parameters of the Standard Model. Furthermore, Renormalization Group Equations are used in order to express the sparticle masses involved, in terms of the gaugino massm 1/2, the universal scalar massm 0 and the trilinear couplingA at the GUT scale. Modifications in the low energy expressions for the squark masses due to a large top Yukawa coupling are also considered. The above results, reconciled with experimental limits are used to put lower bounds on the parametersm 1/2,m 0 and the low energy scalar masses.